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(2) Intermediate 4. Student Edition. Stephen Hake.

(3) ACKNOWLEDGEMENTS. This book was made possible by the significant contributions of many individuals and the dedicated efforts of talented teams at Harcourt Achieve. Special thanks to Chris Braun for conscientious work on Power Up exercises, Problem Solving scripts, and student assessments. The long hours and technical assistance of John and James Hake were invaluable in meeting publishing deadlines. As always, the patience and support of Mary is most appreciated. – Stephen Hake. Staff Credits Editorial: Joel Riemer, Hirva Raj, Paula Zamarra, Smith Richardson, Gayle Lowery, Robin Adams, David Baceski, Brooke Butner, Cecilia Colome, Pamela Cox, James Daniels, Leslie Bateman, Michael Ota, Stephanie Rieper, Ann Sissac, Chad Barrett, Heather Jernt Design: Alison Klassen, Joan Cunningham, Alan Klemp, Julie Hubbard, Lorelei Supapo, Andy Hendrix, Rhonda Holcomb Production: Mychael Ferris-Pacheco, Jennifer Cohorn, Greg Gaspard, Donna Brawley, John-Paxton Gremillion Manufacturing: Cathy Voltaggio, Kathleen Stewart Marketing: Marilyn Trow, Kimberly Sadler E-Learning: Layne Hedrick. ISBN 13: 978-1-6003-2540-3 ISBN 10: 1-6003-2540-8 © 2008 Harcourt Achieve Inc. and Stephen Hake All rights reserved. No part of the material protected by this copyright may be reproduced or utilized in any form or by any means, in whole or in part, without permission in writing from the copyright owner. Requests for permission should be mailed to: Paralegal Department, 6277 Sea Harbor Drive, Orlando, FL 32887. Saxon is a trademark of Harcourt Achieve Inc. 1 2 3 4 5 6 7 8 048 14 13 12 11 10 9 8 7. ii. Saxon Math Intermediate 4.

(4) ABOUT THE AUTHOR Stephen Hake has authored six books in the Saxon Math series. He writes from 17 years of classroom experience as a teacher in grades 5 through 12 and as a math specialist in El Monte, California. As a math coach, his students won honors and recognition in local, regional, and statewide competitions. Stephen has been writing math curriculum since 1975 and for Saxon since 1985. He has also authored several math contests including Los Angeles County’s first Math Field Day contest. Stephen contributed to the 1999 National Academy of Science publication on the Nature and Teaching of Algebra in the Middle Grades. Stephen is a member of the National Council of Teachers of Mathematics and the California Mathematics Council. He earned his BA from United States International University and his MA from Chapman College.. iii.

(5) CONTENTS OVERVIEW. Table of Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . v Letter from the Author . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xvii How to Use Your Textbook . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xviii Problem Solving Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 Section 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 Lessons 1–10, Investigation 1 Section 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67 Lessons 11–20, Investigation 2 Section 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127 Lessons 21–30, Investigation 3 Section 4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 192 Lessons 31–40, Investigation 4 Section 5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 263 Lessons 41–50, Investigation 5 Section 6 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 326 Lessons 51–60, Investigation 6 Section 7 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 394 Lessons 61–70, Investigation 7 Section 8 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 455 Lessons 71–80, Investigation 8 Section 9 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 519 Lessons 81–90, Investigation 9 Section 10. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 578 Lessons 91–100, Investigation 10 Section 11. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 640 Lessons 101–110, Investigation 11 Section 12. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 704 Lessons 111–120, Investigation 12 English/Spanish Math Glossary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 760 Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 809. iv. Saxon Math Intermediate 4.

(6) TA B LE O F CO N T E N T S. TA B L E O F C O N T E N T S Integrated and Distributed Units of Instruction. Section 1. Lessons 1–10, Investigation 1. Lesson. Page. Strands Focus. Problem Solving Overview. 1. NO, PS, CM, C, R. 1. • Review of Addition. 7. NO, A, PS, CM, R. 2. • Missing Addends. 14. NO, A, PS, CM, C, R. 18. NO, A, PS, CM, R. 24. NO, PS, CM, C, R. 29. NO, PS, CM, R. 3. 4. 5. • Sequences • Digits • Place Value Activity Comparing Money Amounts • Ordinal Numbers • Months of the Year. 6. • Review of Subtraction. 35. NO, PS, RP, R. 7. • Writing Numbers Through 999. 39. NO, PS, CM, C. 45. NO, PS, C, R. 8. • Adding Money Activity Adding Money Amounts. 9. • Adding with Regrouping. 50. NO, PS, CM, RP, R. 10. • Even and Odd Numbers. 55. NO, PS, CM, R. 60. NO, CM, C, R. Investigation 1. • Number Lines Activity Drawing Number Lines. Strands Key: NO = Number and Operations A = Algebra G = Geometry. M = Measurement DAP = Data Analysis and Probability PS = Problem Solving CM = Communication. RP = Reasoning and Proof C = Connections R = Representation. Table of Contents. v.

(7) TA B L E O F C O N T E N T S. Section 2. Lessons 11–20, Investigation 2. Lesson. Page. Strands Focus. 11. • Addition Word Problems with Missing Addends. 67. NO, A, PS, C. 12. • Missing Numbers in Subtraction. 72. NO, A, PS, C. 77. NO, PS, CM, C. 82. NO, PS, RP, C. 88. NO, PS, CM, C. 94. NO, A, PS, RP, C. 99. NO, PS, RP, C. 104. M, PS, CM, C. 110. M, PS, CM, C, R. 116. NO, PS, C, R. 122. NO, M, C, R. 13. 14. • Adding Three-Digit Numbers Activity Adding Money • Subtracting Two-Digit and Three-Digit Numbers • Missing Two-Digit Addends. 15. • Subtracting Two-Digit Numbers with Regrouping Activity Subtracting Money. 16. 17. 18. 19 20 Investigation 2. vi. • Expanded Form • More on Missing Numbers in Subtraction • Adding Columns of Numbers with Regrouping • Temperature Activity Measuring Temperature • Elapsed Time Problems Activity Finding Elapsed Time • Rounding • Units of Length and Perimeter Activity Estimating the Perimeter. Saxon Math Intermediate 4.

(8) Lessons 21–30, Investigation 3. Lesson. Page. Strands Focus. 21. • Triangles, Rectangles, Squares, and Circles Activity Drawing a Circle. 127. G, M, C, R. 22. • Naming Fractions • Adding Dollars and Cents Activity Counting Money. 133. NO, PS, CM, C, R. 23. • Lines, Segments, Rays, and Angles Activity Real-World Segments and Angles. 140. G, CM, C, R. 24. • Inverse Operations. 147. NO, A, PS, C, R. 25. • Subtraction Word Problems. 152. A, PS, CM, RP. 26. • Drawing Pictures of Fractions. 158. NO, CM, RP, R. 27. • Multiplication as Repeated Addition • More Elapsed Time Problems Activity Finding Time. 162. NO, M, PS, C, R. 28. • Multiplication Table. 168. NO, CM, C, R. 29. • Multiplication Facts: 0s, 1s, 2s, 5s. 175. NO, PS, CM, C. 30. • Subtracting Three-Digit Numbers with Regrouping Activity Subtracting Money. 179. NO, PS, CM, C. • Multiplication Patterns • Area • Squares and Square Roots Activity 1 Finding Perimeter and Area Activity 2 Estimating Perimeter and Area. 185. NO, M, CM, C, R. Investigation 3. TA B LE O F CO N T E N T S. Section 3. Strands Key: NO = Number and Operations A = Algebra G = Geometry. M = Measurement DAP = Data Analysis and Probability PS = Problem Solving CM = Communication. RP = Reasoning and Proof C = Connections R = Representation. Table of Contents. vii.

(9) TA B L E O F C O N T E N T S. Section 4. Lessons 31–40, Investigation 4. Lesson. Page. Strands Focus. 31. • Word Problems About Comparing. 192. A, PS, C, R. 32. • Multiplication Facts: 9s, 10s, 11s, 12s. 199. NO, CM, C, R. 33. • Writing Numbers Through Hundred Thousands. 205. NO, CM, C, R. 34. • Writing Numbers Through Hundred Millions. 212. NO, CM, C, R. 35. • Naming Mixed Numbers and Money. 218. NO, PS, CM, C, R. 36. • Fractions of a Dollar. 226. NO, CM, C, R. 37. • Reading Fractions and Mixed Numbers from a Number Line. 233. NO, CM, C, R. 38. • Multiplication Facts (Memory Group). 238. NO, PS, CM, C, R. 39. • Reading an Inch Scale to the Nearest Fourth. 243. M, CM, C, R. 249. M, PS, CM, R. 256. NO, CM, C, R. 260. NO, CM, C, R. Activity Make a Ruler and Measure 40. • Capacity. • Tenths and Hundredths Investigation 4A Activity 1 Using Money Manipulatives to Represent Decimal Numbers • Relating Fractions and Decimals Investigation 4B. Activity 2 Using Unit Squares to Relate Fractions and Decimal Numbers Activity 3 Using Decimal Numbers on Stopwatch Displays. viii. Saxon Math Intermediate 4.

(10) Lessons 41–50, Investigation 5. Lesson 41. TA B LE O F CO N T E N T S. Section 5. • Subtracting Across Zero • Missing Factors. Page. Strands Focus. 263. NO, A, RP, C, R. 42. • Rounding Numbers to Estimate. 269. NO, PS, C, R. 43. • Adding and Subtracting Decimal Numbers, Part 1. 276. NO, RP, C, R. 282. NO, RP, C, R. 287. NO, G, RP, C, R. Activity Adding and Subtracting Decimals 44 45. • Multiplying Two-Digit Numbers, Part 1 • Parentheses and the Associative Property • Naming Lines and Segments • Relating Multiplication and Division, Part 1. 46. Activity Using a Multiplication Table to Divide. 294. NO, RP, C, R. 47. • Relating Multiplication and Division, Part 2. 301. NO, A, C, R. 48. • Multiplying Two-Digit Numbers, Part 2. 307. NO, PS, C, R. 49. • Word Problems About Equal Groups, Part 1. 312. NO, A, PS, C. 50. • Adding and Subtracting Decimal Numbers, Part 2. 317. NO, CM, R. 322. NO, RP, R. Activity Adding and Subtracting Decimals Investigation 5. • Percents Activity Percent. Strands Key: NO = Number and Operations A = Algebra G = Geometry. M = Measurement DAP = Data Analysis and Probability PS = Problem Solving CM = Communication. RP = Reasoning and Proof C = Connections R = Representation. Table of Contents. ix.

(11) TA B L E O F C O N T E N T S. Section 6. Lessons 51–60, Investigation 6. Lesson. 51. • Adding Numbers with More Than Three Digits. Page. Strands Focus. 326. NO, RP, R, C. 331. NO, A, RP, CM. 337. NO, RP, CM, R. 344. NO, M, RP, R. 351. NO, RP, R. 359. NO, RP, R. • Checking One-Digit Division. 52. • Subtracting Numbers with More Than Three Digits • Word Problems About Equal Groups, Part 2 • One-Digit Division with a Remainder. 53. Activity Finding Equal Groups with Remainders • The Calendar. 54. 55. 56. • Rounding Numbers to the Nearest Thousand • Prime and Composite Numbers Activity Using Arrays to Find Factors • Using Models and Pictures to Compare Fractions Activity Comparing Fractions. 57. • Rate Word Problems. 364. NO, A, PS, CM. 58. • Multiplying Three-Digit Numbers. 370. NO, A, PS, CM. 59. • Estimating Arithmetic Answers. 376. NO, A, RP, CM. 60. • Rate Problems with a Given Total. 382. NO, A, RP, C. 387. A, DAP, R. Investigation 6. x. • Displaying Data Using Graphs Activity Displaying Information on Graphs. Saxon Math Intermediate 4.

(12) Lessons 61–70, Investigation 7. Lesson 61. 62. TA B LE O F CO N T E N T S. Section 7. • Remaining Fraction • Two-Step Equations • Multiplying Three or More Factors • Exponents. Page. Strands Focus. 394. NO, A, PS, RP. 399. NO, M, C. 63. • Polygons. 405. G, CM, C, R. 64. • Division with Two-Digit Answers, Part 1. 411. NO, PS. 65. • Division with Two-Digit Answers, Part 2. 417. NO, PS, CM, RP. • Similar and Congruent Figures 66. Activity Determining Similarity and Congruence. 424. G, CM, RP, C. 67. • Multiplying by Multiples of 10. 429. NO, CM, RP. 68. • Division with Two-Digit Answers and a Remainder. 435. NO, PS, R. 440. M, CM, RP, C. 446. A, PS, CM, R. 451. DAP, PS, CM, RP, R. 69. 70. Investigation 7. • Millimeters Activity Measuring with Metric Units • Word Problems About a Fraction of a Group • Collecting Data with Surveys Activity Class Survey. Strands Key: NO = Number and Operations A = Algebra G = Geometry. M = Measurement DAP = Data Analysis and Probability PS = Problem Solving CM = Communication. RP = Reasoning and Proof C = Connections R = Representation. Table of Contents. xi.

(13) TA B L E O F C O N T E N T S. Section 8. Lessons 71–80, Investigation 8. Lesson. Page. Strands Focus. 71. • Division Answers Ending with Zero. 455. NO, CM. 72. • Finding Information to Solve Problems. 460. PS, CM, RP, R. 466. G, PS, CM, C. 473. NO, CM, C. 477. G, M, CM, C, R. 484. NO, PS, CM, C. 489. M, CM, C. 496. G, M, PS, CM. 501. G, CM, RP, C. 509. NO, PS, CM. 514. DAP, CM, RP, C, R. 73 74. • Geometric Transformations Activity Using Transformations • Fraction of a Set • Measuring Turns. 75. Activity 1 Rotations and Degrees Activity 2 Rotations and Congruence. 76. • Division with Three-Digit Answers • Mass and Weight. 77. Activity 1 Customary Weight Activity 2 Metric Mass • Classifying Triangles. 78. 79 80. Activity Transformations and Congruent Triangles • Symmetry Activity Reflections and Lines of Symmetry • Division with Zeros in Three-Digit Answers • Analyzing and Graphing Relationships. Investigation 8. Activity 1 Graphing Pay Rates Activity 2 Graphing on a Coordinate Grid. xii. Saxon Math Intermediate 4.

(14) Lessons 81–90, Investigation 9. Lesson 81. TA B LE O F CO N T E N T S. Section 9. • Angle Measures Activity Angle Measurement Tool. Page. Strands Focus. 519. M, C, R. 525. G, PS, C, R. • Tessellations 82. Activity 1 Tessellations Activity 2 Tessellations with Multiple Shapes. 83. • Sales Tax. 532. A, PS, CM, C. 84. • Decimal Numbers to Thousandths. 538. NO, PS, CM, RP. 85. • Multiplying by 10, by 100, and by 1000. 543. NO, CM. 86. • Multiplying Multiples of 10 and 100. 548. NO, PS, CM, C. 87. • Multiplying Two Two-Digit Numbers, Part 1. 552. NO, CM, C. 88. • Remainders in Word Problems About Equal Groups. 558. NO, PS, C. • Mixed Numbers and Improper Fractions 89. Activity Modeling Mixed Numbers and Improper Fractions. 563. NO, PS, R. 90. • Multiplying Two Two-Digit Numbers, Part 2. 568. NO, CM, RP, C. 574. NO, CM, C, R. • Investigating Fractions with Manipulatives Investigation 9. Activity 1 Using Fraction Manipulatives Activity 2 Understanding How Fractions, Decimals, and Percents Are Related. Strands Key: NO = Number and Operations A = Algebra G = Geometry. M = Measurement DAP = Data Analysis and Probability PS = Problem Solving CM = Communication. RP = Reasoning and Proof C = Connections R = Representation. Table of Contents. xiii.

(15) TA B L E O F C O N T E N T S. Section 10. Lessons 91–100, Investigation 10. Lesson 91. • Decimal Place Value. Page. Strands Focus. 578. NO, C, R. 584. G, CM, C, R. • Classifying Quadrilaterals 92. Activity 1 Quadrilaterals in the Classroom Activity 2 Symmetry and Quadrilaterals. 93. • Estimating Multiplication and Division Answers. 591. NO, C. 94. • Two-Step Word Problems. 595. A, PS, CM, RP, C. 95. • Two-Step Problems About a Fraction of a Group. 602. A, CM, RP, R. 96. • Average. 607. DAP, RP, C, R. 97. • Mean, Median, Range, and Mode. 612. DAP, PS, C, R. 618. G, C, R. 624. G, PS, C, R. 630. G, PS, CM, RP. 636. DAP, PS, RP, R. 98. 99. 100. Investigation 10. xiv. • Geometric Solids Activity Geometric Solids in the Real World • Constructing Prisms Activity Constructing Prisms • Constructing Pyramids Activity Constructing Models of Pyramids • Probability Activity Probability Experiments. Saxon Math Intermediate 4.

(16) Lessons 101–110, Investigation 11. Lesson 101. 102. • Tables and Schedules Activity Make a Table • Tenths and Hundredths on a Number Line Activity Measuring Objects with a Meterstick. Page. Strands Focus. 640. M, DAP, C, R. 648. NO, CM, R. 103. • Fractions Equal to 1 and Fractions Equal to 2_1. 654. NO, M, PS, RP, R. 104. • Changing Improper Fractions to Whole or Mixed Numbers. 660. NO, PS, CM, C. 105. • Dividing by 10. 666. NO, C, R. 106. • Evaluating Expressions. 671. A, PS, C. 107. • Adding and Subtracting Fractions with Common Denominators. 675. NO, PS, RP, R. 680. A, M, RP, C. 108. TA B LE O F CO N T E N T S. Section 11. • Formulas • Distributive Property. 109. • Equivalent Fractions. 687. NO, CM, RP, R. 110. • Dividing by Multiples of 10. 694. NO, PS, CM, R. 699. M, PS, CM, RP. • Volume Investigation 11. Activity 1 Estimating Volume Activity 2 Estimating Perimeter, Area, and Volume. Strands Key: NO = Number and Operations A = Algebra G = Geometry. M = Measurement DAP = Data Analysis and Probability PS = Problem Solving CM = Communication. RP = Reasoning and Proof C = Connections R = Representation. Table of Contents. xv.

(17) TA B L E O F C O N T E N T S. Section 12. Lessons 111–120, Investigation 12. Lesson. Page. Strands Focus. 704. M, PS, C, R. • Estimating Perimeter, Area, and Volume 111. Activity 1 Estimating Perimeter and Area Activity 2 Estimating Volume. 112. • Reducing Fractions. 710. NO, CM, PR, R. 113. • Multiplying a Three-Digit Number by a Two-Digit Number. 715. NO, PS, CM, C. 114. • Simplifying Fraction Answers. 720. NO, PS, RP. 115. • Renaming Fractions. 725. NO, PS, CM, C. 116. • Common Denominators. 729. NO, PS, C. 117. • Rounding Whole Numbers Through Hundred Millions. 735. NO, PS, CM, C. 118. • Dividing by Two-Digit Numbers. 741. NO, PS, CM, RP. 119. • Adding and Subtracting Fractions with Different Denominators. 746. NO, PS, CM. 120. • Adding and Subtracting Mixed Numbers with Different Denominators. 750. NO, RP, C, R. 754. NO, A, PS. Investigation 12. xvi. • Solving Balanced Equations Activity Solving Equations. Appendix A. • Roman Numerals Through 39. 756. NO, C, R. Appendix B. • Roman Numerals Through Thousands. 758. NO, C, R. Saxon Math Intermediate 4.

(18) LET TER FROM THE AUTHOR. Dear Student, We study mathematics because it plays a very important role in our lives. Our school schedule, our trip to the store, the preparation of our meals, and many of the games we play involve mathematics. The word problems in this book are often drawn from everyday experiences. When you become an adult, mathematics will become even more important. In fact, your future may depend on the mathematics you are learning now. This book will help you to learn mathematics and to learn it well. As you complete each lesson, you will see that similar problems are presented again and again. Solving each problem day after day is the secret to success. Your book includes daily lessons and investigations. Each lesson has three parts. 1. The first part is a Power Up that includes practice of basic facts and mental math. These exercises improve your speed, accuracy, and ability to do math in your head. The Power Up also includes a problem-solving exercise to help you learn the strategies for solving complicated problems. 2. The second part of the lesson is the New Concept. This section introduces a new mathematical concept and presents examples that use the concept. The Lesson Practice provides a chance for you to solve problems using the new concept. The problems are lettered a, b, c, and so on. 3. The final part of the lesson is the Written Practice. This section reviews previously taught concepts and prepares you for concepts that will be taught in later lessons. Solving these problems will help you practice your skills and remember concepts you have learned. Investigations are variations of the daily lesson. The investigations in this book often involve activities that fill an entire class period. Investigations contain their own set of questions but do not include Lesson Practice or Written Practice. Remember to solve every problem in each Lesson Practice, Written Practice, and Investigation. Do your best work, and you will experience success and true learning that will stay with you and serve you well in the future.. Temple City, California. Letter from the Author. xvii.

(19) HOW TO USE YOUR TE X TBOOK Saxon Math Intermediate 4 is unlike any math book you have used! It doesn’t have colorful photos to distract you from learning. The Saxon approach lets you see the beauty and structure within math itself. You will understand more mathematics, become more confident in doing math, and will be well prepared when you take high school math classes.. LESSON. 69 Power Yourself Up • Millimeters. Start off each lesson by practicing your basic skills and concepts, mental math, and problem solving. Make your math brain stronger by exercising it every day. Soon you’ll know these facts by memory!. Power Up facts. Power Up I. count aloud. Count down by threes from 60 to 3.. mental math. a. Number Sense: 12 × 2 × 10. 240. b. Number Sense: 20 × 20 × 20. 8000. c. Number Sense: 56 + 9 + 120. 185. d. Fractional Parts: What is. 1 2. of $60?. $30. e. Measurement: Six feet is 72 inches. How many inches tall is a person whose height is 5 feet 11 inches? 71 in. f. Measurement: The airplane is 5500 feet above the ground. Is that height greater than or less than 1 mile? greater than g. Estimation: Xavier can read about 30 pages in one hour. If Kevin must read 58 pages, about how long will it take him? (Round your answer to the nearest hour.) 2 hr. Learn Something New!. h. Calculation: 62, − 18, ÷ 9, × 50. problem solving. Each day brings you a new concept, but you’ll only have to learn a small part of it now. You’ll be building on this concept throughout the year so that you understand and remember it by test time.. 100. Choose an appropriate problem-solving strategy to solve this problem. The parking lot charged $1.50 for the first hour and 75¢ for each additional hour. Harold parked the car in the lot from 11:00 a.m. to 3 p.m. How much money did he have to pay? Explain how you found your answer. $3.75; see student work.. New Concept This line segment is one centimeter long: If we divide a centimeter into ten equal lengths, each equal length is 1 millimeter long. A dime is about 1 millimeter thick. 1 millimeter thick 440. Saxon Math Intermediate 4.

(20) Activity Transformations and Congruent Triangles Material needed: • Lesson Activity 31 Formulate For this activity, you will develop a plan to predict the movement of a triangle to determine congruence.. Get Active!. a. Cut out the two right triangles from Lesson Activity 31, or use triangle manipulatives. b.. Place the two triangles in the positions shown below. Plan a way to move one triangle using a translation and a rotation to show that the triangles are congruent. Remember that one triangle must be on top of the other in the final position. Write your conclusion. Include direction and degrees in your answer. Sample: a 90º-clockwise rotation Predict. Dig into math with a handson activity. Explore a math concept with your friends as you work together and use manipulatives to see new connections in mathematics.. and a horizontal translation. c.. Predict Place the two triangles in the positions shown below. Plan a way to move one triangle to show that the triangles are congruent. Remember that one triangle must be on top of the other in the final position. Write your conclusion. Include direction and degrees in your answer. Sample: a. reflection in the horizontal axis, a 90º-clockwise rotation, and a horizontal translation. Lesson Practice a. No. The sides would not meet to form a triangle:. a.. The Lesson Practice lets you check to see if you understand today’s new concept.. Can a right triangle have two right angles? Why. or why not? b. What is the name for a triangle that has at least two sides equal in length? isosceles triangle c.. 498. Conclude. Check It Out!. Model Use a color tile to model a translation, reflection, and rotation. Watch students.. Saxon Math Intermediate 4. Written Practice. Distributed and Integrated. 1. One hundred fifty feet equals how many yards?. 50 yards. (Inv. 2, 71). 2. Tammy gave the clerk $6 to pay for a book. She received 64¢ in change. Tax was 38¢. What was the price of the book? $4.98. (83). Exercise Your Mind!. 3. DaJuan is 2 years older than Rebecca. Rebecca is twice as old as Dillon. DaJuan is 12 years old. How old is Dillon? (Hint: First find Rebecca’s age.) 5 years old. (94). 4. Write each decimal as a mixed number: 295 9 a. 3.295 31000 b. 32.9 3210. (84). When you work the Written Practice exercises, you will review both today’s new concept and also math you learned in earlier lessons. Each exercise will be on a different concept — you never know what you’re going to get! It’s like a mystery game — unpredictable and challenging. As you review concepts from earlier in the book, you’ll be asked to use higher-order thinking skills to show what you know and why the math works. The mixed set of Written Practice is just like the mixed format of your state test. You’ll be practicing for the “big” test every day!. * 5. a.. (Inv. 5, 95). 9 3100. c. 3.09. Three fourths of the 84 contestants guessed incorrectly. How many contestants guessed incorrectly? Draw a picture to illustrate the problem. 63 contestants. 5. 5.. 84 contestants 21 contestants. Represent. b. What percent of the contestants guessed incorrectly? 6. These thermometers show the average daily minimum and maximum temperatures in North Little Rock, Arkansas, during the month of January. What is the range of the temperatures? 18°F. (18, 97). 75%. b. What is the radius of this circle?. inch. 1. 1 2. 21 contestants. did not guess incorrectly.. 21 contestants. 21 contestants. . . . . 7. a. What is the diameter of this circle?. 1 4. guessed incorrectly.. . &. (21). 3 4. &. 1 in. in.. 2. Lesson 100. 633. How to Use Your Textbook. xix.

(21) HOW TO USE YOUR TE X TBOOK. Become Investigator! Become ananInvestigator! Dive into math concepts and explore the depths of math connections in the Investigations. I NVE S TI G ATI O N. Continue to develop your mathematical thinking through applications, activities, and extensions.. 11. Focus on • Volume Shapes such as cubes, pyramids, and cones take up space. The amount of space a shape occupies is called its volume. We measure volume with cubic units like cubic centimeters, cubic inches, cubic feet, and cubic meters.. 1 cubic centimeter. 1 cubic inch. The model of the cube we constructed in Lesson 99 has a volume of one cubic inch. Here is a model of a rectangular solid built with cubes that each have a volume of 1 cubic centimeter. To find the volume of the rectangular solid, we can count the number of cubic centimeters used to build it.. 2 cm 3 cm. 2 cm. One way to count the small cubes is to count the cubes in one layer and then multiply that number by the number of layers. There are six cubes on the top layer, and there are two layers. The volume of the rectangular solid is 12 cubic centimeters. Count cubes to find the volume of each rectangular solid below. Notice the units used in each figure. 2.. 1. 2. 2 ft 8 cubic feet. 3 cm. 2 ft. 2 cm 4 cm 24 cubic centimeters. 3.. 4. 3 in. 3 in.. 4m. 3 in.. 27 cubic inches. 1. 2 ft × 2 ft × 2 ft = 8 cu. ft 2. 4 cm × 2 cm × 3 cm = 24 cu. cm 3. 3 in. × 3 in. × 3 in. = 27 cu. in. 4. 4 m × 3 m × 4 m = 48 cu. m. 4m. 3m. 48 cubic meters Investigation 11. 699.

(22) PROB LE M S OLVI NG OVERVIEW. Focus on • Problem Solving We study mathematics to learn how to use tools that help us solve problems. We face mathematical problems in our daily lives. We can become powerful problem solvers by using the tools we store in our minds. In this book we will practice solving problems every day. This lesson has three parts: Problem-Solving Process The four steps we follow when solving problems. Problem-Solving Strategies Some strategies that can help us solve problems. Writing and Problem Solving Describing how we solved a problem. Four-Step Problem-Solving Process Solving a problem is like arriving at a new location, so the process of solving a problem is similar to the process of taking a trip. Suppose we are on the mainland and want to reach a nearby island.. Step. Problem-Solving Process. Taking a Trip. 1. Understand Know where you are and where you want to go.. We are on the mainland and want to go to the island.. 2. Plan. 3. Solve. 4. Plan your route. Follow the plan.. Check Check that you have reached the right place.. We might use the bridge, the boat, or swim. Take the journey to the island. Verify that we have reached our new location.. Problem-Solving Overview. 1.

(23) When we solve a problem, it helps to ask ourselves some questions along the way. Step. Follow the Process. Ask Yourself Questions. 1. Understand. What information am I given? What am I asked to find or do?. 2. Plan. How can I use the given information to solve the problem? What strategy can I use to solve the problem?. 3. Solve. Am I following the plan? Is my math correct?. 4. Check. Does my solution answer the question that was asked? Is my answer reasonable?. Below we show how we follow these steps to solve a word problem. Example 1 Ricardo arranged nine small congruent triangles in rows to make one large triangle.. 2OWONE 2OWTWO 2OWTHREE. If Ricardo extended the triangle to 5 rows, how many small triangles will there be in row four and row five? Step 1: Understand the problem. Ricardo used nine small congruent triangles. He placed the small triangles so that row one has 1 triangle, row two has 3 triangles, and row three has 5 triangles. We are asked to find the number of small triangles in row four and row five if the large triangle is extended to 5 rows. Step 2: Make a plan. The first row has one triangle, the second row has three triangles, and the third row has five triangles. We see that there is a pattern. We can make a table and continue the pattern to extend the large triangle to five rows. Step 3: Solve the problem. We follow our plan by making a table that shows the number of triangles used in each row if the large triangle is extended to 5 rows. Row Number of Triangles. one. two. three. four. five. 1. 3. 5. 7. 9. +2. +2. +2. +2. We see that the number of small triangles in each row increases by 2 when a new row is added. 5+2=7 2. Saxon Math Intermediate 4. 7+2=9.

(24) This means row four has 7 triangles and row five has 9 triangles. Step 4: Check the answer. We look back at the problem to see if we have used the correct information and have answered the question. We made a table to show the number of small triangles that were in each row. We found a pattern and extended the triangle to 5 rows. We know that row four has 7 small triangles and that row five has 9 small triangles. We can check our answer by drawing a diagram and counting the number of triangles in each row. 2OWONE 2OWTWO 2OWTHREE 2OWFOUR 2OWFIVE. Our answer is reasonable and correct. Example 2 Mr. Jones built a fence around his square-shaped garden. He put 5 fence posts on each side of the garden, including one post in each corner. How many fence posts did Mr. Jones use? Step 1: Understand the problem. Mr. Jones built a square fence around his garden. He put 5 fence posts on each side of the garden. There is one fence post in each corner. Step 2: Make a plan. We can make a model of the fence using paper clips to represent each fence post. Step 3: Solve the problem. We follow our plan by creating a model. First we will show one fence post in each corner.. We know each side has five fence posts. We see that each side of our model already has two fence posts. We add three fence posts to each side to show five posts per side. Each side of the fence now has five posts, including the one in each corner. We find that Mr. Jones used 16 fence posts to build the fence.. Problem-Solving Overview. 3.

(25) Step 4: Check the answer. We look back at the problem to see if we used the correct information and answered the question. We know that our answer is reasonable because each side of the square has 5 posts, including the one in each corner. We also see that there are four corner posts and 3 posts on each of the four sides. Mr. Jones used 16 posts to build the fence. 1. List in order the four steps of the problem-solving process. 1. Understand, 2. Plan, 3. Solve, 4. Check. 2. What two questions do we answer to understand a problem? What information am I given? What am I asked to find or do to solve the problem?. Refer to the following problem to answer questions 3–8. Katie left her house at the time shown on the clock. She arrived at Monica’s house 15 minutes later. Then they spent 30 minutes eating lunch. What time did they finish lunch? 3.. Connect. 4.. Verify. What information are we given? What are you asked to find? time girls finish their lunch. 5. Which step of the four-step problem-solving process did you complete when you answered questions 3 and 4? Step 1: Understand. 6. Describe your plan for solving the problem. 7.. Explain. Solve the problem by following your plan. Show your work. Write your solution to the problem in a way someone else will understand.. 8. Check your work and your answer. Look back to the problem. Be sure you use the information correctly. Be sure you found what you were asked to find. Is your answer reasonable?. Problem-Solving Strategies As we consider how to solve a problem, we choose one or more strategies that seem to be helpful. Referring to the picture at the beginning of this lesson, we might choose to swim, to take the boat, or to cross the bridge to travel from the mainland to the island. Other strategies might not be as effective for the illustrated problem. For example, choosing to walk or bike across the water are strategies that are not reasonable for this situation.. 4. Saxon Math Intermediate 4. 11 10. 12 1 2. 9. 3. 4. 8 7. 6. 5. 3. Katie left her house at 11:15. She arrived at Monica’s house 15 minutes later and spent 30 minutes eating lunch. 6. Sample: I moved the minute hand in a clockwise direction for 15 minutes (11:15 to 11:30). Then I moved the minute hand clockwise again for 30 more minutes (11:30 to 12:00). 7. Katie left at 11:15. Add 15 min—11:30. Add 30 min—12:00. They finished at 12:00 p.m. 8. We started with 11:15 and added 15 minutes and then 30 minutes to get 12:00 p.m., so our answer is reasonable..

(26) When solving mathematical problems we also select strategies that are appropriate for the problem. Problem-solving strategies are types of plans we can use to solve problems. Listed below are ten strategies we will practice in this book. You may refer to these descriptions as you solve problems throughout the year. Act it out or make a model. Moving objects or people can help us visualize the problem and lead us to the solution. Use logical reasoning. All problems require reasoning, but for some problems we use given information to eliminate choices so that we can close in on the solution. Usually a chart, diagram, or picture can be used to organize the given information and to make the solution more apparent. Draw a picture or diagram. Sketching a picture or a diagram can help us understand and solve problems, especially problems about graphs or maps or shapes. Write a number sentence or equation. We can solve many word problems by fitting the given numbers into equations or number sentences and then finding the unknown numbers. Make it simpler. We can make some complicated problems easier by using smaller numbers or fewer items. Solving the simpler problem might help us see a pattern or method that can help us solve the complex problem. Find/Extend a pattern. Identifying a pattern that helps you to predict what will come next as the pattern continues might lead to the solution. Make an organized list. Making a list can help us organize our thinking about a problem. Guess and check. Guessing the answer and trying the guess in the problem might start a process that leads to the answer. If the guess is not correct, use the information from the guess to make a better guess. Continue to improve your guesses until you find the answer. Make or use a table, chart, or graph. Arranging information in a table, chart, or graph can help us organize and keep track of data. This might reveal patterns or relationships that can help us solve the problem.. Problem-Solving Overview. 5.

(27) Work backwards. Finding a route through a maze is often easier by beginning at the end and tracing a path back to the start. Likewise, some problems are easier to solve by working back from information that is given toward the end of the problem to information that is unknown near the beginning of the problem. 9. Name some strategies used in this lesson.. See student work.. The chart below shows where each strategy is first introduced in this textbook. Strategy. Lesson. Act It Out or Make a Model. 1. Use Logical Reasoning. 13. Draw a Picture or Diagram. 9. Write a Number Sentence or Equation. 28. Make It Simpler. 20. Find/Extend a Pattern. 8. Make an Organized List. 46. Guess and Check. 15. Make or Use a Table, Chart, or Graph. 3. Work Backwards. 57. Writing and Problem Solving Sometimes, a problem will ask us to explain our thinking. This helps us measure our understanding of math and it is easy to do. • Explain how you solved the problem. • Explain how you know your answer is correct. • Explain why your answer is reasonable. For these situations, we can describe the way we followed our plan. This is a description of the way we solved Example 1. We made a table and continued a pattern to extend the large triangle to five rows. We found that row four had 7 small triangles and row five had 9 small triangles. 10. Write a description of how we solved the problem in Example 2. See student work.. Other times, we will be asked to write a problem for a given equation. Be sure to include the correct numbers and operations to represent the equation. 11. Write a word problem for 9 + 5 = 14. See student work.. 6. Saxon Math Intermediate 4.

(28) LESSON. 1 • Review of Addition Power Up facts. Power Up A1. count aloud. Count by twos from 2 to 20.. mental math. Add ten to a number in a–f. a. Number Sense: 20 + 10. 30. b. Number Sense: 34 + 10. 44. c. Number Sense: 10 + 53. 63. d. Number Sense: 5 + 10 e. Number Sense: 25 + 10 f. Number Sense: 10 + 8. 15 35 18. g. What number is one less than 36?. problem solving. 35. Six students are planning to ride the roller coaster at the amusement park. Three students can sit in each row of the roller coaster. How many rows will six students fill? Focus Strategy: Act It Out We are told that six students will ride the roller coaster. Three students can sit in each row. We are asked to find the number of rows six students will fill. Understand. Six student volunteers can act out the situation in the problem. Plan. Your teacher will call six students to the front of the classroom and line them up in rows of three. Three students will fill one row of the roller coaster, and three more students will fill a second row of the roller coaster. Since there are no students left over, we know that six students will fill two rows of the roller coaster. Solve. 1. For instructions on how to use the Power Up activities, please consult the preface.. Lesson 1. 7.

(29) We know our answer is reasonable because by acting out the problem, we see that six students divide into two equal groups of three. Each group of three students fills one row. Check. How many rows would six students fill if only two students can sit in each row? 3 rows. New Concept Reading Math We can write an addition number sentence both horizontally and vertically. Write an addition number sentence in horizontal form. Write an addition number sentence in vertical form. Sample: 3 + 4 = 7. 3 +4 7. Addition is the combining of two groups into one group. For example, when we count the dots on the top faces of a pair of dot cubes, we are adding. + 4 four. =. 3 + = plus three equals. 7 seven. The numbers that are added are called addends. The answer is called the sum. The addition 4 + 3 = 7 is a number sentence. A number sentence is a complete sentence that uses numbers and symbols instead of words. Here we show two ways to add 4 and 3: 4 addend + 3 addend 7 sum. 3 addend + 4 addend 7 sum. Notice that if the order of the addends is changed, the sum remains the same. This is true for any two numbers and is called the Commutative Property of Addition. When we add two numbers, either number may be first. 4+3=7. 3+4=7. When we add zero to a number, the number is not changed. This property of addition is called the Identity Property of Addition. If we start with a number and add zero, the sum is identical to the starting number. 4+0=4. 8. Saxon Math Intermediate 4. 9+0=9. 0+7=7.

(30) Example 1 Write a number sentence for this picture: A number sentence for the picture is 4 + 5 = 9. The number sentence 5 + 4 = 9 is also correct. When adding three numbers, the numbers may be added in any order. Here we show six ways to add 4, 3, and 5. Each way the answer is 12. 4 3 +5 12. 4 5 +3 12. 3 4 +5 12. 3 5 +4 12. 5 4 +3 12. 5 3 +4 12. Example 2 Show six ways to add 1, 2, and 3. We can form two number sentences that begin with the addend 1. 1+2+3=6. 1+3+2=6. We can form two number sentences that begin with the addend 2. 2+1+3=6. 2+3+1=6. We can form two number sentences that begin with the addend 3. 3+1+2=6. 3+2+1=6. Many word problems tell a story. Some stories are about putting things together. Read this story: D’Jon had 5 marbles. He bought 7 more marbles. Then D’Jon had 12 marbles. Reading Math We translate the problem using an addition formula. D’Jon had: 5 marbles He bought some more: 7 marbles Total: 12 marbles. There is a plot to this story. D’Jon had some marbles. Then he bought some more marbles. When he put the marbles together, he found the total number of marbles. Problems with a “some and some more” plot can be expressed with an addition formula. A formula is a method for solving a certain type of problem. Below is a formula for solving problems with a “some and some more” plot: Formula Some + Some more Total. Problem 5 marbles + 7 marbles 12 marbles. Lesson 1. 9.

(31) Here we show the formula written horizontally: Formula: Some + Some more = Total Problem: 5 marbles + 7 marbles = 12 marbles A story can become a word problem if one or more of the numbers is missing. Here are three word problems: D’Jon had 5 marbles. He bought 7 more marbles. Then how many marbles did D’Jon have? D’Jon had 5 marbles. He bought some more marbles. Then D’Jon had 12 marbles. How many marbles did D’Jon buy? D’Jon had some marbles. He bought 7 more marbles. Then D’Jon had 12 marbles. How many marbles did D’Jon have before he bought the 7 marbles? To solve a word problem, we can follow the four-step problem-solving process. Step 1: Read and translate the problem. Step 2: Make a plan to solve the problem. Step 3: Follow the plan and solve the problem. Step 4: Check your answer for reasonableness. A plan that can help us solve word problems is to write a number sentence. We write the numbers we know into a formula. Example 3 Matias saw 8 ducks. Then he saw 7 more ducks. How many ducks did Matias see in all? This problem has a “some and some more” plot. We write the numbers we know into the formula. Formula: Some + Some more = Total Problem: 8 ducks + 7 ducks = Total We may shorten the number sentence to 8 + 7 = t. Math Symbols Any uppercase or lowercase letter may be used to represent a number. For example, we can use T or t to represent a total.. 10. We find the total by adding 8 and 7. Matias saw 15 ducks in all. One way to check the answer is to see if it correctly completes the problem. Matias saw 8 ducks. Then he saw 7 more ducks. Matias saw 15 ducks in all.. Saxon Math Intermediate 4.

(32) Example 4 Samantha saw 5 trees in the east field, 3 trees in the west field, and 4 trees in the north field. How many trees did Samantha see in all? In this story there are three addends. Formula Some Some more + Some more Total. Problem 5 trees 3 trees + 4 trees Total. Using addition, we find that Samantha saw 12 trees in all. We check the answer to see if it is reasonable. There are three addends: 5 trees, 3 trees, and 4 trees. When we put all the trees together, we add 5 + 3 + 4. The number of trees is 12. Some of the problems in this book will have an addend missing. When one addend is missing and the sum is given, the problem is to find the missing addend. What is the missing addend in this number sentence? + 2 two. + plus. = ? ?. = equals. 7 seven. Since we know that 2 + 5 = 7, the missing addend is 5. A letter can be used to represent a missing number, as we see in the example below. Example 5 Find each missing addend: a.. 4 +n 7. b. b + 6 = 10. a. The letter n stands for a missing addend. Since 4 + 3 = 7, the letter n stands for the number 3 in this number sentence. b. In this problem, the letter b is used to stand for the missing addend. Since 4 + 6 = 10, the letter b stands for the number 4.. Lesson 1. 11.

(33) Lesson Practice. Add: a. 5 + 6 11. b. 6 + 5. d. 4 + 8 + 6 18 f. 13 laps; 5 laps + 8 laps = total or 5 + 8=t h. 1 + 3 + 5 = 9, 1 + 5 + 3 = 9, 3 + 1 + 5 = 9, 3 + 5 + 1 = 9, 5 + 1 + 3 = 9, 5+3+1=9 k. addend + addend = sum addend. 11. c. 8 + 0. e. 4 + 5 + 6. 8. 15. f. D’Anya ran 5 laps in the morning. She ran 8 laps in the afternoon. How many laps did she run in all? Write a number sentence for this problem. g.. h.. Write two number sentences for this picture to show the Commutative Property. 2 + 4 = 6, 4 + 2 = 6 Formulate. List. Show six ways to add 1, 3, and 5.. Find each missing addend: i. 7 + n = 10 3 k.. + addend. j. a + 8 = 12. 4. Copy these two patterns on a piece of paper. In each of the six boxes, write either “addend” or “sum.” Connect. sum +. +. =. Distributed and Integrated. Written Practice. Write a number sentence for problems 1 and 2. Then solve each problem. Formulate. * 1. There were 5 students in the first row and 7 students in the second row. How many students were in the first two rows? 5 students + 7 students = total or 5 + 7 = t; 12 students. * 2. Ling had 6 coins in her left pocket and 3 coins in her right pocket. How many coins did Ling have in both pockets? 6 coins + 3 coins = total or 6 + 3 = t; 9 coins. Find each sum or missing addend: 3. 9 + 4 13 * 5.. 4 +n 9. 5. 4. 8 + 2 * 6.. w +5 8. 3. * 7.. 6 +p 8. 10. 2. * 8.. q +8 8. 0. Beginning in this lesson, we star the exercises that cover challenging or recently presented content. We encourage students to work first on the starred exercises with which they might want help, saving the easier exercises for last.. 12. Saxon Math Intermediate 4.

(34) 9. 3 + 4 + 5. 12. 10. 4 + 4 + 4. 12. 11. 6 + r = 10. 4. 12. x + 5 = 6. 1. 13.. 5 5 +5. 14.. 8 0 +7. 15. 17.. 15. 18.. m 1 + 9 10. 21. 3 + 2 + 5 + 4 + 6. 9 + f 12. 16.. 9 9 +9. 15. 19.. 3. z +5 10. 27. 20.. 5. 0 3 +n 3. 14. Write a number sentence for each picture:. * 23.. * 24.. 6 + 3 = 9 (or 3 + 6 = 9). * 25.. 6 5 +4. 20. 22. 2 + 2 + 2 + 2 + 2 + 2 + 2 Represent. 15.. Sample: 4 + 5 + 2 = 11. List Show six ways to add 2, 3, and 4. 2 + 3 + 4 = 9, 2 + 4 + 3 = 9, 3 + 2 + 4 = 9, 3 + 4 + 2 = 9, 4 + 2 + 3 = 9, 4 + 3 + 2 = 9. * 26. Multiple Choice Sometimes a missing number is shown by a shape instead of a letter. Choose the correct number for △ in the following number sentence: B △ + 3 = 10 A 3 B 7 C 10 D 13 * 27. * 28. * 29. * 30.. Draw a dot cube picture to show 5 + 6.. Represent. Connect. à. Write a horizontal number sentence that has a sum of 17.. Sample: 9 + 8 = 17 Connect. Write a vertical number sentence that has a sum of 15.. Write and solve an addition word problem using the numbers 10 and 8. See student work.. Sample:. 8 +7 15. Formulate. Lesson 1. 13.

(35) LESSON. 2 • Missing Addends Power Up facts. Power Up A. count aloud. Count by fives from 5 to 50.. mental math. For a–f, add ten to a number. a. Number Sense: 40 + 10. 50. b. Number Sense: 26 + 10. 36. c. Number Sense: 39 + 10. 49. d. Number Sense: 7 + 10. 17. e. Number Sense: 10 + 9. 19. f. Number Sense: 10 + 63. 73. g. What number is one less than 49?. problem solving. 48. Choose an appropriate problem-solving strategy to solve this problem. Maria, Sh’Meika, and Kimber are on a picnic. They want to draw sketches of the clouds in the sky. Sharon brought 15 sheets of paper and 6 pencils to share with the other two girls. How many sheets of paper and how many pencils can each girl have if they share equally? 5 sheets of paper and 2 pencils. New Concept Thinking Skill Discuss. What is another way you can find the number of the third roll? Sample: subtract 8 from 12. 14. Derek rolled a dot cube three times. The picture below shows the number of dots on the top face of the cube for each of the first two rolls. Represent. First roll. Second roll. The total number of dots on all three rolls was 12.. Saxon Math Intermediate 4.

(36) Math Language An equation is a number sentence that uses the symbol = to show that two quantities are equal. Here are two examples: 5+2=7 6+n=8 These are not equations: 5+2 4>6. Let’s draw a picture to show the number of dots on the top face of the cube for Derek’s third roll. We will write a number sentence, or an equation, for this problem. The first two numbers are 5 and 3. We do not know the number of the third roll, so we will use a letter. We know that the total is 12. 5 + 3 + t = 12 To find the missing addend, we first add 5 and 3, which makes 8. Then we think, “Eight plus what number equals twelve?” Since 8 plus 4 equals 12, the third roll was .. Example Find each missing addend: a.. Visit www. SaxonMath.com/ Int4Activities for a calculator activity.. 6 n +5 17. b. 4 + 3 + 2 + b + 6 = 20. a. We add 6 and 5, which makes 11. We think, “Eleven plus what number equals seventeen?” Since 11 plus 6 equals 17, the missing addend is 6. b. First we add 4, 3, 2, and 6, which equals 15. Since 15 plus 5 is 20, the missing addend is 5.. Lesson Practice. Find each missing addend: a. 8 + a + 2 = 17 7. b. b + 6 + 5 = 12. 1. c. 4 + c + 2 + 3 + 5 = 20 6. Written Practice. Distributed and Integrated. Write a number sentence for problems 1 and 2. Then solve each problem. Formulate. 1. * 1. Jordan’s rabbit, Hoppy, ate 5 carrots in the morning and 6 carrots in the (1) afternoon. How many carrots did Hoppy eat in all? 5 carrots + 6 carrots = total or 5 + 6 = t; 11 carrots 1. The italicized numbers within parentheses underneath each problem number are called lesson reference numbers. These numbers refer to the lesson(s) in which the major concept of that particular problem is introduced. If additional assistance is needed, refer to the discussion, examples, or practice problems of that lesson.. Lesson 2. 15.

(37) * 2. Five friends rode their bikes from the school to the lake. They rode (1) 7 miles and then rested. They still had 4 miles to go. How many miles was it from the school to the lake? 7 miles + 4 miles = total or 7 + 4 = t; 11 miles Find each sum or missing addend: 3. 9 + n = 13. 4. 7 + 8. 4. (1). 5. (1). * 9. (2). 13. (1). p 7 +6 13. 8 b +3 16. 5. * 6. (2). 10. (1). (2). 5 3 +t 10. 9 7 +3. 14.. 2 m +4 9. 18.. 8 4 +6. (2). 17. 17.. 5 5 2 +w 12. 7.. (1). 4 8 +5. 2. (1). 11. (1). (1). 3. 2 9 +6. 12. (1). 5 3 +q 9. 1. 19.. 2 x +7 11. 2. (2). 3 8 +2 13. 15. (2). 9 3 +7 19. 17. 18. * 21. 5 + 5 + 6 + 4 + x = 23. 8.. 17. 19. 9 5 +3. 15. (1). 16.. 2 3 +r 7. 20.. 5 2 +6. (2). (1). 13. 3. (2). * 22. (1). List Show six ways to add 4, 5, and 6. 4 + 5 + 6 = 15, 4 + 6 + 5 = 15, 5 + 4 + 6 = 15, 5 + 6 + 4 = 15, 6 + 4 + 5 = 15, 6 + 5 + 4 = 15. Represent. Write a number sentence for each picture: Sample: 4 + 2 + 5 = 11. * 23. (1). 24. (1). 16. 5 + 2 = 7 (or 2 + 5 = 7). Saxon Math Intermediate 4. 2.

(38) 25.. What is the name of the answer when we add?. Verify. (1). sum. * 26. Multiple Choice Which number is in the following number (1) sentence? A 6+ = 10 A 4 * 27.. B 6. * 28. (1). 29.. Connect. (1). à. à. Write a horizontal number sentence that has a sum of 20.. Sample: 10 + 10 = 20 Connect. (1). * 30.. D 16. Draw a picture to show 6 + 3 + 5. Sample:. Represent. (2). *. C 10. Write a vertical number sentence that has a sum of 24. Sample:. 12 + 12 24. Write and solve an addition word problem using the numbers 7, 3, and 10. See student work. Word problems may include Formulate. adding 7 and 3 for a sum of 10, or adding 7, 3, and 10 for a sum of 20.. Early Finishers Real-World Connection. There were 35 pictures at the art exhibit. The pictures were made using oils, pastels, or watercolors. Thirteen of the pictures were made using watercolors. An equal number of pictures were made using oils as were made using pastels. How many pictures were made using pastels? Explain how you found the answer. 11 pictures were made using pastels; sample: I wrote the equation 13 + n + n = 35; 35 − 13 = 22; 11 + 11 = 22.. Lesson 2. 17.

(39) LESSON. 3 • Sequences • Digits Power Up facts. Power Up A. count aloud. Count by twos from 2 to 40.. mental math. Number Sense: Add ten, twenty, or thirty to a number in a–f. a.. 20 + 20. d.. 24 + 30. b.. 23 + 20. e.. 50 + 30. 40. 54. 43 + 10. f.. 10 + 65. 43. 53. 80. g. What number is one less than 28?. problem solving. c.. 75 27. Kazi has nine coins to put in his left and right pockets. Find the ways Kazi could place the coins in his left and right pockets. Focus Strategy: Make a Table We are told that Kazi has nine coins that he can put in his left and right pockets. We are asked to find the ways Kazi could place the coins in his left and right pockets. Understand. If Kazi puts all nine coins in his left pocket, he would have zero coins for his right pocket. This means “9 left, 0 right” is a possibility. If Kazi moves one coin from the left pocket to his right pocket, eight coins would remain in his left pocket (9 – 1 = 8). This possibility would be “8 left, 1 right.” We begin to see that there are multiple ways Kazi can put the coins into his left and right pockets. We can make a table to organize the ways Kazi could place the coins. Plan. 18. Saxon Math Intermediate 4.

(40) Number of Coins. We make a table with one column labeled “left” and the other labeled “right.” We start by writing the combinations we have already found. Then we fill in new rows until we finish the table. Solve. Notice that the sum of the numbers in each row is 9. Also notice that there are ten rows, which means there are ten different ways Tom could put the coins into his left and right pockets. We know our answer is reasonable because Kazi can put from 0 to 9 coins in one pocket and the rest in the other pocket, which is ten ways. We made a table to help us find all the ways. Check. Left. Right. 9. 0. 8. 1. 7. 2. 6. 3. 5. 4. 4. 5. 3. 6. 2. 7. 1. 8. 0. 9. What is another problem-solving strategy that we could use to solve the problem? We could act out the problem with real coins.. New Concepts Sequences. Counting is a math skill we learn early in life. Counting by ones we say, “one, two, three, four, five, . . . .”. Reading Math. 1, 2, 3, 4, 5, . . .. The three dots written after a sequence such as 1, 2, 3, 4, 5, … mean that the sequence continues without end even though the numbers are not written.. These numbers are called counting numbers. The counting numbers continue without end. We may also count by numbers other than one. Counting by twos: 2, 4, 6, 8, 10, . . . Counting by fives: 5, 10, 15, 20, 25, . . . These are examples of counting patterns. A counting pattern is a sequence. A counting sequence may count up or count down. We can study a counting sequence to discover a rule for the sequence. Then we can find more numbers in the sequence.. Example 1 Find the rule and the next three numbers of this counting sequence: 10, 20, 30, 40,. ,. ,. , .... The rule is count up by tens. Counting this way, we find that the next three numbers are 50, 60, and 70.. Lesson 3. 19.

(41) Example 2 Find the rule of this counting sequence. Then find the missing number in the sequence. 30, 27, 24, 21,. , 15, . . .. The rule is count down by threes. If we count down three from 21, we find that the missing number in the sequence is 18. We see that 15 is three less than 18, which follows the rule.. Digits. To write numbers, we use digits. Digits are the numerals 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. The number 356 has three digits, and the last digit is 6. The number 67,896,094 has eight digits, and the last digit is 4.. Example 3 The number 64,000 has how many digits? The number 64,000 has five digits. Example 4 What is the last digit of 2001? The last digit of 2001 is 1. Example 5 How many different three-digit numbers can you write using the digits 1, 2, and 3? Each digit may be used only once in every number you write. Model. We can act out the problem by writing each digit on a separate slip of paper. Then we vary the arrangement of the slips until all of the possibilities have been discovered. We can avoid repeating arrangements by writing the smallest number first and then writing the rest of the numbers in counting order until we write the largest number. 123, 132, 213, 231, 312, 321 We find we can make six different numbers.. Lesson Practice. Write the rule and the next three numbers of each counting sequence: Generalize. a. 10, 9, 8, 7,. 6. ,. 5. ,. 4. , . . . count down by ones. b. 3, 6, 9, 12, 15 , 18 , 21 , . . . count up by threes. 20. Saxon Math Intermediate 4.

(42) Connect. Find the missing number in each counting sequence:. c. 80, 70, 60 , 50, . . .. d. 8, 12 , 16, 20, 24, . . .. How many digits are in each number? e. 18 2 digits. f. 5280. 4 digits. g. 8,403,227,189 10 digits. What is the last digit of each number? h. 19 9. i. 5281. 1. j. 8,403,190. 0. k. How many different three-digit numbers can you write using the digits 7, 8, and 9? Each digit may be used only once in every number you write. List the numbers in counting order. six numbers; 789, 798, 879, 897, 978, 987. Written Practice Formulate. Distributed and Integrated. Write a number sentence for problems 1 and 2. Then solve each. problem. * 1. Diana has 5 dollars, Sumaya has 6 dollars, and Britt has 7 dollars. (1) Altogether, how much money do the three girls have? $5 + $6 + $7 = total or 5 + 6 + 7 = t; 18 dollars. * 2. On Taye’s favorite CD there are 9 songs. On his second-favorite CD (1) there are 8 songs. Altogether, how many songs are on Taye’s two favorite CDs? 9 songs + 8 songs = total or 9 + 8 = t; 17 songs * 3. How many digits are in each number? (3) a. 593 3 digits b. 180 3 digits. c. 186,527,394. * 4. What is the last digit of each number? (3) a. 3427 7 b. 460 0. c. 437,269. 9 digits. 9. Find each missing addend: 5. 5 + m + 4 = 12. 3. (2). Conclude. 6. (2). Write the next number in each counting sequence:. * 7. 10, 20, 30, 40 , . . . (3). * 9. 40, 35, 30, 25, 20 , . . . (3). * 6. 8 + 2 + w = 16. * 8. 22, 21, 20, 19 , . . . (3). * 10. 70, 80, 90, 100 , . . . (3). Lesson 3. 21.

(43) Generalize. Write the rule and the next three numbers of each counting sequence:. * 11. 6, 12, 18, 24 , 30 , 36 , . . . count up by sixes (3). 12. 3, 6, 9, 12 , 15 , 18 , . . . count up by threes (3). 13. 4, 8, 12, 16 , 20 , 24 , . . . count up by fours (3). * 14. 45, 36, 27, 18 ,. 9. , 0 , .... (3). Connect. count down by nines. Find the missing number in each counting sequence: * 16. 12, 18, 24 , 30, . . .. * 15. 8, 12, 16 , 20, . . . (3). (3). 18. 6, 9, 12 , 15, . . .. 17. 30, 25, 20 , 15, . . . (3). (3). 19. How many small rectangles are shown? Count by twos. (3). 16 small rectangles. 20. How many X s are shown? Count by fours. 24 X s (3). * 21. (1). 22. (1). Represent. XX XX. XX XX. XX XX. XX XX. XX XX. Write a number sentence for the picture below.. Sample: 3 + 6 + 4 = 13. 4 8 7 +5. 23. (1). 24. 9 5 7 + 8. Saxon Math Intermediate 4. 24. (1). 29. * 26. Multiple Choice If = 3 and (1) the following? D A 3 B 4. 22. XX XX. 25.. 8 4 7 + 2. (1). 2 9 7 + 5 23. 21. = 4, then C 5. +. equals which of D 7.

(44) * 27. How many different arrangements of three letters can you write using (3) the letters a, b, and c? The different arrangements you write do not need to form words. six arrangements; abc, acb, bac, bca, cab, cba * 28. (1). * 29.. Write a horizontal number sentence that has a sum of 9.. Connect. Sample: 3 + 6 = 9. Write a vertical number sentence that has a sum of 11.. Connect. (1). * 30. (1). Formulate. sum of 12.. Early Finishers Real-World Connection. Sample:. Write and solve an addition word problem that has a. 4 +7 11. See student work.. Ivan noticed that the first three house numbers on the right side of a street were 2305, 2315, and 2325. a. What pattern do you see in this list of numbers? b. If this pattern continues, what will the next three house numbers be? c. The houses on the left side of the street have corresponding numbers that end in 0. What are the house numbers for the first 6 houses on the left side of the street? d. What pattern is used for the house numbers on the left side of the street? a. The house numbers increase by 10 beginning with 2305; b. 2335, 2345, 2355; c. 2300, 2310, 2320, 2330, 2340, 2350; d. the house numbers increase by 10 beginning with 2300.. Lesson 3. 23.

(45) LESSON. 4 • Place Value Power Up facts. Power Up A. count aloud. Count by fives from 5 to 100.. mental math. Add ten, twenty, or thirty to a number in a–f.. Number of Coins Left. Right. 7. 2. 6. 3. 5. 4. 4. 5. 3. 6. 2. 7. problem solving. a. Number Sense: 66 + 10. 76. b. Number Sense: 29 + 20. 49. c. Number Sense: 10 + 76. 86. d. Number Sense: 38 + 30. 68. e. Number Sense: 20 + 6 f. Number Sense: 40 + 30. 26 70. g. Add 10 to 77 and then subtract 1. What is the final answer? 86 Choose an appropriate problem-solving strategy to solve this problem. Lorelei has a total of nine coins in her left and right pockets. She has some coins (at least two) in each pocket. Make a table that shows the possible number of coins in each pocket.. New Concept To learn place value, we will use money manipulatives and pictures to show different amounts of money. We will use $100 bills, $10 bills, and $1 bills. Model. 24. Saxon Math Intermediate 4.

(46) Example 1 Write the amount of money that is shown in the picture below.. Since there are 2 hundreds, 4 tens, and 3 ones, the amount of money shown is $243. Example 2 Use money manipulatives or draw a diagram to show $324 using $100 bills, $10 bills, and $1 bills. Model. To show $324, we use 3 hundreds, 2 tens, and 4 ones.. 3 hundreds Math Language We can use money to show place value because our number system and our money system are both base-ten systems.. 2 tens. 4 ones. The value of each place is determined by its position. Three-digit numbers like 324 occupy three different places. ones place tens place hundreds place 3 2 4. Activity Thinking Skill Connect. What does the zero in $203 represent? What does the zero in $230 represent?. Comparing Money Amounts Materials needed: • money manipulatives from Lesson Activities 2, 3, and 4 Use money manipulatives to show both $203 and $230. Write the amount that is the greater amount of money. Model. Sample: no $10 bills; no $1 bills. Lesson 4. 25.

(47) Example 3 The digit 7 is in what place in 753? The 7 is in the third place from the right, which shows the number of hundreds. This means the 7 is in the hundreds place.. Lesson Practice a.. 100 10 hundreds 3 tens. 1 1 one. a.. Use money manipulatives or draw a diagram to show $231 using $100 bills, $10 bills, and $1 bills.. b.. Use money manipulatives or draw a diagram to $100 $10 show $213. Which is less, $231 or $213?. Model. Model. 2 hundreds 1 ten. $213 is less than $231.. The digit 6 is in what place in each of these numbers? c. 16 ones. d. 65. e. 623. tens. hundreds. f. Use three digits to write a number equal to 5 hundreds, 2 tens, and 3 ones. 523. Written Practice. Distributed and Integrated. 1. When Roho looked at the group of color tiles, he saw 3 red, 4 blue, (1) 5 green, and 1 yellow. How many color tiles were there in all? Write the number sentence to find the answer. 13 tiles; 3 + 4 + 5 + 1 = t * 2. (1). Represent. 6 + 6 = 12. Write a number sentence for this picture:. 3. How many cents are in 4 nickels? Count by fives.. 20 cents. (3). 5¢. 5¢. 5¢. 5¢. Find each sum or missing addend: 4. (1). 4 +n 12. 5.. 8. (1). 4 5 +3. 6. 13 (1) +y 19. 7.. 6. (1). 12. * 8. 4 + n + 5 = 12. 3. (2). 26. Saxon Math Intermediate 4. 9. n + 2 + 3 = 8 (2). 3. 7 +s 14. 7. $1 3 ones. ;.

(48) Generalize. Write the rule and the next three numbers of each counting sequence:. * 10. 9, 12, 15, 18 , 21 , 24 , . . .. count up by threes. (3). * 11. 30, 24, 18, 12 ,. 6. (3). ,. 0. , .... count down by sixes. * 12. 12, 16, 20, 24 , 28 , 32 , . . .. count up by fours. * 13. 35, 28, 21, 14 ,. count down by sevens. (3). 7. (3). ,. 0. , .... 14. How many digits are in each number? (3) a. 37,432 5 digits b. 5,934,286. 7 digits. * 15. What is the last digit of each number? (3) a. 734 4 b. 347 7 * 16. (4). Represent. and $1 bills.. c. 453,000. c. 473. 6 digits. 3. Draw a diagram to show $342 in $100 bills, $10 bills, 100 3 hundreds. 10 4 tens. 1 2 ones. 17. How much money does this picture show?. $434. (4). Connect. Find the missing number in each counting sequence:. 18. 24, 30 , 36, 42, . . . (3). * 19. 36, 32, 28 , 24, . . . (3). * 20. How many ears do 10 rabbits have? Count by twos.. 20 ears. (3). * 21. The digit 6 is in what place in 365?. tens. (4). * 22. (1). Represent. Write a number sentence for this picture:. 5 + 6 = 11 (or 6 + 5 = 11). 23. Find the missing addend: (2). 2 + 5 + 3 + 2 + 3 + 1 + n = 20. 4. Lesson 4. 27.

(49) * 24. (2). Explain. How do you find the missing addend in problem 23?. Sample: I add all the known addends and then count on 4 more from 16 to total 20. 6 + 7 + 8 = 21, 6 + 8 + 7 = 21, 7 + 6 + 8 = 21, 7 + 8 + 6 = 21, 8 + 6 + 7 = 21, 8 + 7 + 6 = 21. 25. Show six ways to add 6, 7, and 8. (1). * 26. Multiple Choice In the number 123, which digit shows the number of (4) hundreds? A A 1 B 2 C 3 D 4 * 27.. Predict. (3). What is the tenth number in the counting sequence below? 1, 2, 3, 4, 5, . . .. 10. * 28. How many different three-digit numbers can you write using the digits (3) 2, 5, and 8? Each digit may be used only once in every number you write. List the numbers in counting order. six numbers; 258, 285, 528, 582, 825, 852. * 29.. Connect. (1). * 30. (1). Write a number sentence that has addends of 6 and 7. 6 + 7 = 13 or. Write and solve an addition word problem using the numbers 2, 3, and 5. See student work. Word problems may include adding Formulate. 2 and 3 for a sum of 5, or adding 2, 3, and 5 for a sum of 10.. Early Finishers Real-World Connection. Andres was asked to solve this riddle: What number am I? I have three digits. There is a 4 in the tens place, a 7 in the ones place, and a 6 in the hundreds place. Andres said the answer was 467. Did Andres give the correct answer? Use money manipulatives to explain your answer. No, Andres did not give the correct answer. There should be six hundreds, four tens, and seven ones. The answer to the riddle should be 647.. 28. Saxon Math Intermediate 4. 6 +7 13.

(50) LESSON. 5 • Ordinal Numbers • Months of the Year Power Up facts. Power Up A. count aloud. Count by fours from 4 to 40.. mental math. Number Sense: Add a number ending in zero to another number in a–e. a.. 24 + 60. d.. 33 + 30. 84. Number of Coins Left. Right. 2. 7. 3. 6. 4. 5. problem solving. 63. b.. 36 + 10. c.. 46. 50 + 42 92. e.. 40 + 50 90. f. Add 10 to 44 and then subtract 1. What is the final answer? 53 g. Add 10 to 73 and then subtract 1. What is the final answer? 82 Choose an appropriate problem-solving strategy to solve this problem. Farica has a total of nine coins in her left and right pockets. She has some coins (at least two) in each pocket. She has more coins in her right pocket than in her left pocket. Make a table that shows the possible number of coins in each pocket.. New Concepts Ordinal Numbers. If we want to count the number of children in a line, we say, “one, two, three, four, . . . .” These numbers tell us how many children we have counted. To describe a child’s position in a line, we use words like first, second, third, and fourth. Numbers that tell position or order are called ordinal numbers.. Lesson 5. 29.

(51) Example 1 There are ten children in the lunch line. Pedro is fourth in line. a. How many children are in front of Pedro?. Math Language Ordinal numbers tell which one. Which one is Pedro? He is the fourth person.. b. How many children are behind him? A diagram may help us understand the problem. We draw and label a diagram using the information given to us. Pedro. Cardinal numbers tell how many. How many people are in front of Pedro? There are 3 people in front of Pedro.. in front. fourth. behind. a. Since Pedro is fourth in line, we see that there are three children in front of him. b. The rest of the children are behind Pedro. From the diagram, we see that there are six children behind him. Ordinal numbers can be abbreviated. The abbreviation consists of a counting number and the letters st, nd, rd, or th. Here we show some abbreviations: first .......... 1st. sixth ........ 6th. eleventh ....... 11th. second..... 2nd. seventh ... 7th. twelfth.......... 12th. third ......... 3rd. eighth ..... 8th. thirteenth ..... 13th. fourth ....... 4th. ninth ....... 9th. twentieth...... 20th. fifth .......... 5th. tenth ....... 10th. twenty-first .. 21st. Example 2 Andy is 13th in line. Kwame is 3rd in line. How many students are between Kwame and Andy? We begin by drawing a diagram. Kwame. Andy. third. thirteenth. From the diagram we see that there are nine students between Kwame and Andy.. 30. Saxon Math Intermediate 4.

(52) Months of the Year. We use ordinal numbers to describe the months of the year and the days of each month. The table below lists the twelve months of the year in order. A common year is 365 days long. A leap year is 366 days long. The extra day in a leap year is added to February every four years. Month. Math Language Thirty days have September, April, June, and November. All the rest have 31, except February, which has 28.. Order. Days. January. first. 31. February. second. March. third. 31. April. fourth. 30. May. fifth. 31. June. sixth. 30. July. seventh. 31. August. eighth. 31. September. ninth. 30. October. tenth. 31. November. eleventh. 30. December. twelfth. 31. 28 or 29. When writing dates, we can use numbers to represent the month, day, and year. For example, if Adolfo was born on the twenty-sixth day of February in 1998, then he could write his birth date this way: 2/26/98 The form for this date is “month/day/year.” The 2 stands for the second month, which is February, and the 26 stands for the twenty-sixth day of the month. Example 3 J’Nae wrote her birth date as 7/8/99. a. In what month was J’Nae born? b. In what year was she born? a. In the United States, we usually write the number of the month first. The first number J’Nae wrote was 7. She was born in the seventh month, which is July. b. We often abbreviate years by using only the last two digits of the year. We assume that J’Nae was born in 1999.. Lesson 5. 31.

(53) Example 4 Mr. Chitsey’s driver’s license expired on 4/29/06. Write that date using the name of the month and all four digits of the year. The fourth month is April, and “06” represents the year 2006. Mr. Chitsey’s license expired on April 29, 2006.. Lesson Practice. a. Jayne was third in line, and Zahina was eighth in line. How many people were between them? Draw a picture to show the people in the line. 4 people; see student work. b. Write your birth date in month/day/year form. See student work. c. In month/day/year form, write the date that Independence Day will next be celebrated. 7/4/(year). Written Practice * 1. (1). Distributed and Integrated. At the grocery store there were 5 people in the first line, 6 people in the second line, and 4 people in the third line. Altogether, how many people were in the three lines? Write a number sentence to find the answer. 15 people; 5 + 6 + 4 = t Formulate. Find each missing addend: 2.. 2 6 +x 15. 6.. 2 5 +w 10. (2). (2). 7. 3.. 1 6 y +7 14. 4.. 3 4 z +5 12. 5.. 1 6 n +6 13. 7.. 2 +a 7. 8.. r 6 +5 11. 9.. 3 +t 5. (2). 3. (1). 5. (2). (1). (2). (1). 2. * 10. Tadeo was born on 8/15/93. Write Tadeo’s birth date using the name of (5) the month and all four digits of the year. August 15, 1993 Conclude. Write the rule and the next three numbers of each counting sequence:. 11. 12, 15, 18, 21 , 24 , 27 , . . . (3). 32. Saxon Math Intermediate 4. count up by threes.

(54) 12. 16, 20, 24, 28 , 32 , 36 , . . .. count up by fours. (3). * 13. 28, 35, 42, 49 , 56 , 63 , . . .. count up by sevens. (3). * 14. Find the missing number: 30, 36 , 42, 48 (3). * 15. (3). * 16. (4). * 17. (1). How did you find the missing number in problem 14?. Explain. Sample: I counted up by 6; 42 + 6 = 48 and 30 + 6 = 36.. Draw a diagram to show $432 in $100 bills, $10 bills,. Represent. and $1 bills. Represent. 100 4 hundreds. 10 3 tens. 1 2 ones. Write a number sentence for the picture below.. 5 + 5 + 5 = 15. 18. The digit 8 is in what place in 845?. hundreds. (4). * 19. (4). * 20. (3). Use three digits to write the number that equals 2 hundreds plus 3 tens plus 5 ones. 235 Represent. Predict. number?. If the pattern is continued, what will be the next circled 12. 1, 2, 3 , 4, 5, 6 , 7, 8, 9 , 10, . . . 21. Seven boys each have two pets. How many pets do the boys have? (3) Count by twos. 14 pets 22. (1). 5 8 4 7 4 +3 31. 23. (1). 5 7 3 8 4 +2 29. 24. (1). 9 7 6 5 4 +2 33. 25. (1). 8 7 3 5 4 +9 36. * 26. Multiple Choice Jenny was third in line. Jessica was seventh in line. (5) How many people were between Jenny and Jessica? A A 3 B 4 C 5 D 6. Lesson 5. 33.

(55) 27.. Predict. (3). What is the tenth number in this counting sequence? 2, 4, 6, 8, 10, . . .. 20. * 28. How many different arrangements of three letters can you write using (3) the letters r, s, and t? The different arrangements you write do not need to form words. six arrangements; rst, rts, srt, str, trs, tsr * 29. *. Connect. (1). * 30. (1). Write a number sentence that has addends of 5 and 4.. 5 + 4 = 9 or. 5 +4 9. Write and solve an addition word problem using the numbers 1, 9, and 10. See student work. Word problems may include adding 1 Formulate. and 9 for a sum of 10, or adding 1, 9, and 10 for a sum of 20.. Early Finishers Real-World Connection. 34. During the fourth month of every year, Stone Mountain Park near Atlanta, Georgia, hosts Feria Latina, one of the largest Hispanic cultural events in the state. What is the name of the month in which Feria Latina is held? If Amy and Carlos attend the festival next year on the 21st of the month, how would you write that date in month/date/year form? April; 4/21/20XX. Saxon Math Intermediate 4.

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